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Question
ΔABC is an isosceles triangle with AB = AC. GB and HC ARE perpendiculars drawn on BC.
Prove that
(i) BG = CH
(ii) AG = AH
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Solution
In ΔABC
AB = AC
∠ABC = ∠ACB ...(equal sides have equal angles opposite to them)...(i)
∠GBC = ∠HCB = 90° ........(ii)
Subtracting (i) from (ii)
∠GBA = ∠HCA..........(iii)
In ΔGBA and ΔHCA
∠GBA = ∠HCA ...(from iii)
∠BAG - ∠CAH ...(vertically opposite angles)
BC = BC
Therefore, ΔGBA ≅ ΔHCA ...(ASA criteria)
Hence, BG = CH and AG = AH.
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